Clustered failure time data in survival analysis

Survival analysis is a collection of statistical methods for analyzing data where the outcome variable is the time until the occurrence of an event of interest. The time is called "failure time" or "survival time". Here, the event of interest could be any case of researcher's interest, such as death, illness, repetition, response to treatment, deterioration. Cox regression model is one of the most used models in survival analysis. The Cox regression model, first considered by Cox in 1972, is a semi-parametric method and is also known as a proportional hazards model. Clustered failure time data occurs when failures of the units in the same cluster tend to be related. Such data are often encountered in biomedical and epidemiological studies. In classical statistical methods, units are assumed to be independent from each other. However, in some applications, data may also be correlated. In order to make an unbiased and effective prediction, it is necessary to take into account the correlation between the units. The Cox regression model is known as the standard model for classical clustered failure time. In the analysis of the clustered failure time, there are two different approaches, marginal models and conditional models, which gained popularity in recent years. In this study, the statistical techniques used for analyzing clustered failure times were investigated. The methods in the literature were examined in detail and made comparisons between the methods. An application was carried out by using the tire data of big trucks used by Demir Export A.Ş. and obtained results were interpreted.